Various techniques are designed and employed in the petroleum industry for the purpose of placing sand proppant in hydraulically induced fractures to enhance oil or gas flow through a reservoir to the wellbore. Hydraulic fracturing of petroleum reservoirs typically improves fluid flow to the wellbore, thus increasing production rates and ultimate recoverable reserves. A hydraulic fracture is created by injecting a fluid down the borehole and into the targeted reservoir interval at an injection rate and pressure sufficient to cause the reservoir rock within the selected depth interval to fracture in a vertical plane passing through the wellbore. A sand proppant is typically introduced into the fracturing fluid to prevent fracture closure after completion of the treatment and to optimize fracture conductivity.
Since these fracturing techniques are performed at relatively large depths under the Earth's surface, it can be difficult to predict or determine the distribution of sand proppant throughout a network of fractures within the wellbore. To realistically predict and simulate the effects of hydraulic fracturing processes, an accurate, and stable computational simulation of flows through the fracture network is needed. Some existing computational methods may utilize numerical methods to provide estimated flow simulations for fracture networks that are approximated as having relatively simple geometries.
Unfortunately, existing computational methods for modeling dynamic flows of fracture fluid and proppant through a fracture network have several drawbacks when used to model complex fracture networks. For example, large complex dynamic fracture networks (DFNs) may feature fractures with aperture areas that vary by orders of magnitude with respect to each other. The aperture areas can reach very small values in some parts of the DFN regions, thus causing existing numerical processes to become unstable. These numerical processes can become especially unstable for a hydro-fracturing process that extends for many hours of real time simulations.